669 



Physics. — "On the qw'stlon lohether at the absolute zero entropy 

 c/inn(jes on nn,vin<i." By Dr. W. H. Keksom. Supplement N". 33 

 to the Coinmmiicatiorjs IVoiri the Physical Laboratory at Leiden. 

 (Communicated by Prof. H. Kamkrlingh Onnes). 



§ 1. The formula for the entropy of the "gramme-molecide" of 

 a mixture of ideal, not reacting gases, for each of which pV=^RT 

 is valid, contains the expression 



— R2c,\vic,, . ....... (1) 



if Ci represents the number of gramme-molecules of the tirst com- 

 ponent, c, that of the second component etc., which are present in 

 the gramme-molecule of the mixture. 2 will indicate in this paper 

 a summation over the different components. 



The expression (1) passes unchanged into the formula for the 

 entropy of the mixture, when this is transferred from an ideal gas 

 condition as considered above into other conditions. 



Accoi'ding to Planck's version of the Neknst heat theorem the 

 entropy of a one-component substance in a condensed state approaches 

 to a tinite value, which is independent of the pressure and of the 

 special state of aggregation, when the absolute temperature approaches 

 to 0. That value may be taken as a suitable zei'o point for the 

 entropy of that substance in tlie condensed state. 



As it is not immediately evident, how the other terms which 

 occur in the expressioji for tlie entropy of a mixture, can on ap- 

 proaching to 7'=0 furnish a compensation of the term written 

 above, it might be imagined, that for a mixture on approaching to 

 2'=^0 the entropy might not become 0, notwithstanding this is the 

 case for the components. 



In that case, however, at a temperature which differs little from 

 the absolute zero, any reversible isothermal change of the compo- 

 nents, in a condensed state, individually would be connected with 

 a development or absorption of heat, which approaches more rapidly 

 to than the temperature. The reversible mixing of those components, 

 on the other hand, would be accompanied by a heat-effect, which 

 approaches to as rapidly as (eventually more slowly than) the 

 temperature. In other words the mixing heat would be of a different 

 order of magnitude from the heat of each reversible isothermal 

 process performed with the components individually. 



It seems to me that it is more natural to assume, that also fora 

 mixture the entropy at the absolute zero point is equal to 0, if this 

 is the case for the components by the choice of this point as a 

 zero point for the corresponding entropies. 



43 



Proceedings Royal Acad. Amsterdam. Vol. XVI. 



